The Union of Jewish Students of France -- French acronym UEJF -- charged Dick Costolo, chief executive officer of the online messaging service, was "responsible for racial defamation and publicly inciting to discrimination, hate or violence toward Jews," the Jewish Telegraphic Agency reported Monday.
The complaint concerns tweets calling for the killing of Jews and praising the Holocaust.
UEJF sued Twitter last month for $50 million for refusing to follow a French judge's order in January to divulge users who had posted anti-Semitic comments. The student group had brought the suit.
The court also ordered Twitter to create a system for flagging and removing similar comments.
Twitter said in October it had removed the offensive tweets after messages with the hashtag #UnBonJuif ("A Good Jew") became the third most popular hashtag on French Twitter.